A consistent and versatile computational approach for general fluid‐structure‐contact interaction problems

We present a consistent approach that allows to solve challenging general nonlinear fluid‐structure‐contact interaction (FSCI) problems. The underlying formulation includes both “no‐slip” fluid‐structure interaction as well as frictionless contact between multiple elastic bodies. The respective interface conditions in normal and tangential orientation and especially the role of the fluid stress within the region of closed contact are discussed for the general problem of FSCI. A continuous transition of tangential constraints from no‐slip to frictionless contact is enabled by using the general Navier condition with varying slip length. Moreover, the fluid stress in the contact zone is obtained by an extension approach as it plays a crucial role for the lift‐off behavior of contacting bodies. With the given continuity of the formulation, continuity of the discrete system of equations for any variation of the coupled system state (which is essential for the convergence of Newton's method) is reached naturally. As topological changes of the fluid domain are an inherent challenge in FSCI configurations, a noninterface fitted cut finite element method (CutFEM) is applied to discretize the fluid domain. All interface conditions, that is the “no‐slip” FSI, the general Navier condition, and frictionless contact are incorporated using Nitsche based methods, thus retaining the consistency of the model. To account for the strong interaction between the fluid and solid discretization, the overall coupled discrete system is solved monolithically. Numerical examples of varying complexity are presented to corroborate the developments. In a first example, the fundamental properties of the presented formulation such as the contacting and lift‐off behavior, the mass conservation, and the influence of the slip length for the general Navier interface condition are analyzed. Beyond that, two more general examples demonstrate challenging aspects such as topological changes of the fluid domain, large contacting areas, and underline the general applicability of the presented method.